Abstract:Let $X$ and $E$ be a Banach space and a real Banach lattice, respectively, and let $\Gamma $ denote an infinite set. We give concise proofs of the following results: (1) The dual space $X^*$ contains an isometric copy of $c_0$ iff $X^*$ contains an isometric copy of $\ell _\infty $, and (2) $E^*$ contains a lattice-isometric copy of $c_0(\Gamma )$ iff $E^*$ contains a lattice-isometric copy of $\ell _\infty (\Gamma )$.
Keywords: isometry, embedding of $\ell _\infty $, dual space, Banach lattice
AMS Subject Classification: 46B04, 46B25, 47B65